Question

An investor having a risk aversion coefficient (A) equal to 2.5 is considering three portfolios of varying risk and return as shown in the table below. Assuming a risk-free rate equal to 4%, which statement below is CORRECT?

Investment Table

Portfolio	Return	Volatility	Sharpe Ratio
Low Risk	7%	10%	0.30
Medium Risk	10%	20%	0.30
High Risk	13%	30%	0.30

Utility of High Risk Portfolio = 1.75%

A. Of the three portfolios, the Low Risk portfolio provides the highest utility to the investor.

B. All three portfolios provide the same utility to the invdstor since they all have the same Sharpe ratio and lie on the Capital Allocation Line (CAL)

C. Of the three portfolios, the Medium Risk portfolio provides the highest utility to the investor.

D. Of the three portfolios, the High Risk portfolio provides the highest utility to the investor.

Answer 1

Of the three portfolios, the Low Risk portfolio provides the highest utility to the investor

Expected Utility score of Low risk portfolio = Expected return - 0.5 * (Volatility)² * Risk Aversion coefficient

Expected Utility score of Low risk portfolio = 7% - (0.5 * (10%)² * 2.5)

Expected Utility score of Low risk portfolio = 5.75%

Expected Utility score of Medium risk portfolio = Expected return - 0.5 * (Volatility)² * Risk Aversion coefficient

Expected Utility score of Medium risk portfolio = 10% - (0.5 * (20%)² * 2.5)

Expected Utility score of Medium risk portfolio = 5%

Expected Utility score of High risk portfolio = 1.75%